Related papers: Robust Estimation Under Heterogeneous Corruption R…
Robust estimation under Huber's $\epsilon$-contamination model has become an important topic in statistics and theoretical computer science. Statistically optimal procedures such as Tukey's median and other estimators based on depth…
The problem we concentrate on is as follows: given (1) a convex compact set $X$ in ${\mathbb{R}}^n$, an affine mapping $x\mapsto A(x)$, a parametric family $\{p_{\mu}(\cdot)\}$ of probability densities and (2) $N$ i.i.d. observations of the…
We present an extension to the robust phase estimation protocol, which can identify incorrect results that would otherwise lie outside the expected statistical range. Robust phase estimation is increasingly a method of choice for…
We study the algorithmic robustness of general finite Markov chains in terms of their stationary distributions to general, adversarial corruptions of the transition matrix. We show that for Markov chains admitting a spectral gap, variants…
We consider a distributionally robust stochastic optimization problem and formulate it as a stochastic two-level composition optimization problem with the use of the mean--semideviation risk measure. In this setting, we consider a single…
Two models are introduced to investigate graph matching in the presence of corrupt nodes. The weak model, inspired by biological networks, allows one or both networks to have a positive fraction of molecular entities interact randomly with…
We consider the robust phase retrieval problem of recovering the unknown signal from the magnitude-only measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise. We propose a new…
Robust and sparse estimation of linear regression coefficients is investigated. The situation addressed by the present paper is that covariates and noises are sampled from heavy-tailed distributions, and the covariates and noises are…
Highly robust and efficient estimators for the generalized linear model with a dispersion parameter are proposed. The estimators are based on three steps. In the first step the maximum rank correlation estimator is used to consistently…
We study the optimal sample complexity of variable selection in linear regression under general design covariance, and show that subset selection is optimal while under standard complexity assumptions, efficient algorithms for this problem…
In this work we solve the problem of robustly learning a high-dimensional Gaussian mixture model with $k$ components from $\epsilon$-corrupted samples up to accuracy $\widetilde{O}(\epsilon)$ in total variation distance for any constant $k$…
We study the fundamental problems of Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination. Our main contribution is the design of the first sample near-optimal and almost linear-time…
We construct and analyze an estimator of association between random variables based on their similarity in both direction and magnitude. Under special conditions, the proposed measure becomes a robust and consistent estimator of the linear…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
We show that when a high-dimensional data matrix is the sum of a low-rank matrix and a random error matrix with independent entries, the low-rank component can be consistently estimated by solving a convex minimization problem. We develop a…
This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regularized and unregularized cases, when high dimensional data are…
Depth estimation from monocular images is pivotal for real-world visual perception systems. While current learning-based depth estimation models train and test on meticulously curated data, they often overlook out-of-distribution (OoD)…
We study the fundamental problem of estimating the mean of a $d$-dimensional distribution with covariance $\Sigma \preccurlyeq \sigma^2 I_d$ given $n$ samples. When $d = 1$, \cite{catoni} showed an estimator with error $(1+o(1)) \cdot…
This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for…
We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized singlescale model to such multiscale…